Doctor Repulsor - Ludicrous Speed Distance

[ElementUser]

I got this from Norroar in a PM - looks like a solid formula.


I've recently created a formula to calculate the distance of Doctor Repulsors' "Ludicrous Speed". It's quite simple, and so far, it seems to be working and correct!
(However, please do say if you see a mistake)

x = ( 0.93 * y - 15 ) / ( ( 10 + 0.01 * y ) / 100 - z / f )

DISTANCE = ( 0.93 * MANA - 15 ) / ( ( 10 + 0.01 * MANA ) / 100 - MANA REGEN / SPEED )

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Example 1:



(Doctor Repulsor - No items - Level 11)

Mana: 689
Mana Reg.: 2.13
Ludicrous Speed: 1875 units/s

x = ( 0.93 * 689 - 15 ) / ( ( 10 + 0.01 * 689 ) / 100 - 2.13 / 1875 )

x = ~3730 Example 2:


(Doctor Repulsor - No items - Level 25)

Mana: 1417
Mana Reg.: 4.37
Ludicrous Speed: 2500 units/s

x = ( 0.93 * 1417 - 15 ) / ( ( 10 + 0.01 * 1417 ) / 100 - 4.37 / 2500 )

x = ~5429Since you now have the total distance you can travel, you can easily calculate the damage output. Example: 5429*0.16*0.752 = ~653 damage!

--

Thank you for your time, and I hope you will find use of it. I was incapable of finding any threads which would seem appropriate, or any guides containing this information. Figured you might know where to put it!

Sincerely,
Norroar

[Chrysaetos]

Wonder if it's actually possible to get mana regen high enough to be able to go on forever...

I need to test it with 6 Bloodstones with 99 charges each...

[VonL`]

Wonder if it's actually possible to get mana regen high enough to be able to go on forever...

I need to test it with 6 Bloodstones with 99 charges each...

Tested it, doesnt let you go on forever. But it helps quite a bit

[ElementUser]

Theoretically, the denominator must be equal to 0 or less in order to have infinite distance. In other words, the mana regen/speed must be equal to (10 + 0.01 * mana)/100

[daggius]

the map is a finite space tho so u have to stop briefly at the edges to change direction

most mana intensive task u could do would to queue up a bunch of trips between opposite corners of the minimap

are bloodstones capped at 99 charges?

cause if they aren't then you could keep going forever with enough bloodstone charges

[DiktatorN]

grab a regen rune and you can go on until the regen rune have stopped give you mana :P

[Ascer]

6 Sac Stones with 99 charges.

With the regen from the well I got from the legion well to the hellbourne well untill I went oom

[Anderbad]

The problem with using bloodstones is that they increase your maximum mana as well as your regeneration; while increasing the maximum mana would normally allow you to travel slightly further due to the constant 10 attached to the drain, it helps to mitigate your regen by increasing the rate at which mana is drained per unit of distance.

Edit: Obviously enough bloodstones with enough charges will get you wherever you could possibly need to go, but we were discussing the possibility of infinite travel distance.

[Ascer]

Yeah but the mana regen from sac stone is just insane compared to any other item, even if sac stone gives more mana

[Josefin96]

Wouldn't it be easy making a mod out of this? - just make it throw in the numbers in the formula and have the result viewed somewhere.

[ElementUser]

Yes it would, go request one in the Mods section

[RAlCHU]

Wonder if it's actually possible to get mana regen high enough to be able to go on forever...

I need to test it with 6 Bloodstones with 99 charges each...

On rank 1 ultimate do you actually regenerate mana in your ultimate. On rank 2 can you travel corner to corner for half your mana and on rank 3 can you almost travel corner to corner.

maybe little offtopic ;)

[ElementUser]

If you get 6 Sacrificial Stones and try to max 99 charges on all of them, you'll only get 3 of the Sac Stones maxed out (for some reason the game engine doesn't want to let you accumulate charges on the other 3).

But that was last patch so I'm not sure if this still holds true.

[Quzzap]

Tried with 6x99 sacrificial stones, which got me 619.7 mana regen and 3232 max mana. (thats on lv16).

I believe you need to keep your maximum mana as low as possible, and your mana regen as high as possible to achieve unlimited ludicrous speed (mana wise).
The maximum length you can travel is (on Caldavar) about sqrt(16384^2 + 16384^2) = 23170.475. (the Caldavar map is 16384 by 16384 units)
This means the maximum damage you can deal is 23170.475 * 0.16 * 0.752 = 2787.871552
This can be achieved with 6x Restoration Stones.

However, this will not give you infinite ludicrous speed.
You can have your part of fun in practice mode with my Test++ mod that can boost your MP Regen gain from intelligence (times 10 is default) to achieve this.
Now you need to get a higher (10% of your maximum mana) mana regen per second then what you need to ult.

Two examples to achieve this:
lv20 and 10 levels in Attribute Boost and 6x Restoration Stone.
lv25 and 3 levels in Attribute Boost and 6x Restoration Stone.

The lv25 example gets you 670.9 mana regen with only 1677 max mana which results in a higher mana regen per second then you use (1677 / 2500) * 1000 = 670.8 mana per second required to ult.

[CSDragon]

If you get 6 Sacrificial Stones and try to max 99 charges on all of them, you'll only get 3 of the Sac Stones maxed out (for some reason the game engine doesn't want to let you accumulate charges on the other 3).

But that was last patch so I'm not sure if this still holds true.

Did you try dropping the three, filling up your other 3 and picking the old ones back up?

[ElementUser]

I already tried that :(.

Oh well, maybe it was just a glitch back then - haven't retested since.

[Sheriff]

You gotta charge the sac stones 1 at a time

then drop the full one

I have done it many times to reach 6 charged ones O.o

[_RaZieL_]

You gotta charge the sac stones 1 at a time

then drop the full one

I have done it many times to reach 6 charged ones O.o

Or you could create 6 legionnaires to do your dirty work for you, then you only have to kill 99 torturers lol

[Masmaattack]

Or you can just buy 5 x flying cours with the stone and have the hovering near where you kill them and keep a stone on urself, BAM you got 6 x 99 capped stones.

[Imbisill]

with 6 99x charged sacri stones, I went across the full map with ludicrous. You can't gain charges on all of them at the same time if you have them on you however.

[mindspank]

Let f(x) denote the mana available at the time x seconds. Then since the mana usage of Ludicrous Speed is linear in the amount of time used we have

f(x) = f(0) + f'(x)x.

We further see that f(0) = 0.93M - 15, where M denotes the maximal amount of mana, which is just the initial cost of casting the spell. One can readily check that

f'(x) = "mana regen/s" - "mana usage/s" = MR - S/100*(10 + 0.01M),

where MR is the heroes mana regen, S is the Ludicrous Speed level. Simplifying everything we arrive at

f(x) = 0.93M - 15 + (MR - S/100*(10 + 0.01M))x

and we run out of mana at x = (15 - 0.93M)/(MR - S/100(10 + 0.01M)) seconds. Multiplied by S simplifies to



Distance traveled = (15 - 0.93M)/(MR/S - (10 + 0.01M)/100)

M = Maximum mana
I = Intellect
MR = Mana regen
S = Ludicrous travel speedwhich gives the total distance traveled. As Norroar has computed.

[KARTlK]

You should probably make some graphs and tables bro.

I would but I don't even own excel so yeah.

[ElementUser]

Well there are 3 variables, so you're going to have to keep at last 1 of them constant if you want to plot a graph we can see :).

[Josefin96]

Looked pretty interesting so I made a formula for this as well. I just wrote it down in one line so there's not really any more calculation than this made - but it gives the same answers as the formula in the opening post.

d=100(0.93m+r(d/s)-15)/(10+0.01m)

where d: is distance, m: maximal mana, r: mana regeneration and s: speed.

[mindspank]

Looked pretty interesting so I made a formula for this as well. I just wrote it down in one line so there's not really any more calculation than this made - but it gives the same answers as the formula in the opening post.

d=100(0.93m+r(d/s)-15)/(10+0.01m)

where d: is distance, m: maximal mana, r: mana regeneration and s: speed.

That is not the same. And that's why, when you come up with a formula, you must prepare to prove it or at least justify why it is like it is.

[Josefin96]

That is not the same. And that's why, when you come up with a formula, you must prepare to prove it or at least justify why it is like it is.
You're wrong - it does give the same answer. As for why I didn't justify or prove how or why: I merely wrote it down in a single line and didn't think much more of it than so - I simply didn't bother explaining anything of it - but if you so dearly want me to do so, then I'll do it just for you.

d = 100(0.93m+r(d/s)-15)/(10+0.01m)

where: d: is distance, m: max mana, s: travel speed, and r: mana regeneration per second.

(0.93m+r(d/s)-15) is the amount of mana available for the whole travel included the mana regenerated during it.
0.93m-15 is the mana remaining after the initial spell cost.
r(d/s) is the mana regenerated per second multiplied with the ratio of the distance travelled to the travelling speed.
(10+0.01m) is the mana cost per 100 range travelled.
(0.93m+r(d/s)-15)/(10+0.01m) is the ratio of mana available to the mana cost per 100 range travelled.
100(0.93m+r(d/s)-15)/(10+0.01m) is the ratio of the mana available to the mana cost per 100 range travelled multiplied with 100 - giving the max range travelled.

I didn't bother to simplify the equation both because I didn't find it interesting enough at that time but also because the original equation shows the reasoning behind it much clearer than a simplified version of it.
Here under I have simplified it.

d = 100(0.93m+r(d/s)-15)/(10+0.01m)
d = 100(0.93m-15)/(10+0.01m)+100rd/s/(10+0.01m)
ds(10s+0.01ms) = 100s(0.93m-15)+100rd
d(s(10+0.01m)-100r) = 100s(0.93m-15)
d = 100s(0.93m-15)/(s(10+0.01m)-100r)

100s(0.93m-15)/(s(10+0.01m)-100r) gives identical answers as both the formula in the opening post and yours.

[mindspank]

http://img811.imageshack.us/img811/614/drrepulsor.jpg

Legend: Intelligence is the total amount of intelligence your hero has, Distance is the distance in HoN units you travel having full mana and using Ludicrious Speed one until you end up with 0 mana. The Mana Regen on the x-axis is not MR in the formula above. It's the mana regen percentage you get from items and is a percentage. If you simply have 1 mana regen item, say a manatube then your Mana Regen would be 100 %.

Note: We assume theres no Ring of Teacher or Glacius aura present. The graph shows the distance travelled from using a level 3 ultimate. Level 2 and 1 differ by a negligible amount only.

[Josefin96]

Why would you use intelligence and % mana regeneration instead of plain mana and mana regeneration? The mana and mana regeneration values from the intelligence and additonal percentage mana regeneration values can easily be calculated, and you would still be able to add additional mana from plain mana boosters and additional static mana regeneration.

[mindspank]

Why would you use intelligence and % mana regeneration instead of plain mana and mana regeneration? The mana and mana regeneration values from the intelligence and additonal percentage mana regeneration values can easily be calculated, and you would still be able to add additional mana from plain mana boosters and additional static mana regeneration.

The reason is twofold.

I like to think in terms of items I have equipped, for example what happens if I get a null stone and a sheep stick. Then I should have roughly 90 base intelligence, 15 from null stone and 35 from intelligence which amounts to 140 intelligence. Look it up on the y-axis and youre set. Now if you multiply that by 13 you have your mana. They are related bijectively. How often do you think in terms of how large your mana pool is in a game rather than what items you have?

Also if you consider pure mana regeneration as is calculated by the game which includes intelligence, mana regeneration items and static regeneration auras it gets much harder to caclulate your mana regeneration on the fly. There are only two static regeneration auras as far as I know, Glacius aura and Ring of the Teacher. Both give negigible amounts of mana regeneration if youre at a high level. And in any case, you won't be running around with a Ring of the Teacher on DR often. All thats left to calculating the pure mana regeneration is your intelligence and mana regeneration items. Since we already have intelligence on the y-axis it just suffices to add your mana regeneration items.

It's just a more natural point of view.

[Josefin96]

There is Abyssal Skull and Nome's Wisdom as well that gives static mana regeneration but they don't stack (Abyssal skull gives 0.8 mana per second, and Nome's Wisdom).

As for static mana regeneration being negligible: any reasonable amount of mana regeneration is negligible.

I don't agree with intelligence and mana regeneration percentage being easier to calculate with than with mana and mana regeneration. Mana and mana regeneration values are both shown in the game and can be taken right from there, actually being even easier to use as you wouldn't have to add up the mana regenearion percentage, and will then give the correct results even with any added additional mana and or static mana regeneration aura.

[mindspank]

Then I'd suggest you to make your own graph. Sir.

[Hellii]

mind = blown

[JustANGRY]

nobody really answered the topic wich would be int or regen you should max and don't tell me get sac stone...

[Josefin96]

nobody really answered the topic wich would be int or regen you should max and don't tell me get sac stone...

Just read the ****ing thread. The equation depends on 2 variables (not counting travel speed) which means each of their relative effect is going to depend on the other. As for good items for the ultimate: Sheepstick, orchid or stormpspirit - whichever use-effect you find the best.

[GrimmShado]

Math. It works!!!
Seriously, tough, the point is not to max one. If you managed to get low low int but high high regen, you'll get the lowest cost per second, but also your number of seconds would be limited. On the other hand maxing in is a bad idea too, because you get a higher manacost, and your max mana can't keep up. As you can see in the thread the max distance is quite high with ridiculous items for real play, so the conventional way works really fine.
In my opinion the way the skill is coded is to prevent exactly infinite leaping, but allow good distance on good items. So this is a mechanics "curiosity", but in real play, get anything that gives good mana regen and it will give you some int, most of the time. And with one or two int luxury you can do amazing things with ludicrous speed.

[DorkBasher]

i love dr and play him a lot however i have come to terms with the fact that i will never be able to fly fountain to fountain. With that being said it is reasonable to expect to be able to fly to your first tier tower from your fountain with good items. the impact damage is about 1000 magic damage. upon landing however, being completely mana drained, you can be ready for another leap in around 30 seconds (example, (75mana/sec)(30sec)= 2250mana or about a full tank)

side note. my dr build is as follows.

steamboots(who needs post haste when you can fly!), nullstone, codex, spellshards, sheepstick, and then a situational (sacstone, hellflower, FWS, shrunken, harkons) i level shards and codex as needed and get sheepstick as a third item only if the game really demands it.

sideside note, overload stacks with all orbs so with FWS your overload hits more like a movement stun than slow.

[ElementUser]

Keep strategy talk to a minimum

[MetaBrain]

(...)expect to be able to fly to your first tier tower from your fountain with good items. the impact damage is about 1000 magic damage.(...)

Sorry? WTF?:doct:

[PuK]

I had trouble to understand how the formula was matching the skill description. But then i just realised that was because how it was presented.
The following presentation feel much clearer for me. (maybe for others aswell)
Correct me if it's wrong

DISTANCE = ( ( 0.93 * MANA - 15 ) / ( 10 + 0.01 * MANA ) ) * ( 100 - MANA REGEN / SPEED )

As opposed to

DISTANCE = ( 0.93 * MANA - 15 ) / ( ( 10 + 0.01 * MANA ) / 100 - MANA REGEN / SPEED )

I my presentation you multiply both mana requirements(initial+during flight) per 100 units by 100+the mana u can regen meanwhile.
In the OP description you divide the initial jump mana requirement by the mana u require during the flight per 100 units divided by 100+ mana u can regen meanwhile

[ElementUser]

http://www.wolframalpha.com/input/?i=x+%3D+(+0.93+*+y+-+15+)+/+(+(+10+%2B+0.01+*+y+)+/+100+-+z+/+f+)

No ambiguity.

Just apply basic math "BEDMAS" and you'll be fine.

[PuK]

Ho yea, i see the problem now.

It's just that when i was doing both calculation, i obtained a slightly different result, i just didn't realise it was different (i was like "3700 somthing *then 2 min later with the other formula* and 3700 something, ok good same result")
So i just figured it was the same but written differently.
It's just that my presentation seemed much more intuitive to me. But i see my problem now, the "start jump" mana requirement takes 0 sec to do, so there is no reason for it to be influenced by the mana reg/speed. ^^

ty m8